In this paper, we introduce the concepts of 1-prime ideals and 2-prime ideals in semirings. We have also introduced $m_{1}$-system and $m_{2}$-system in semiring. We have shown that if $Q$ is an ideal in the semiring $R$ and if $M$ is an $m_{2}$-system of $R$ such that $overline{Q} igcap M = emptyset$ then there exists as 2-prime ideal $P$ of $R$ such that $Q subseteq P$ with $Pigcap M = emptyset.$}

Keywords: Semirings, Prime ideal, Semiprime ideal